alt Hacker NewsfMRI is a step above dowsing rods. It's plugging a multimeter into an outlet and guessing what type and brand of appliances you are running in your house.
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I was at a talk maybe 15 years ago in which the speaker gave pretty convincing evidence that given a time series of voltages you could learn a lot of things about what kind of appliances you've got running.
I'd say you're right about any given individual channel: the activation of a single voxel doesn't tell us much about all the fancy computation happening in that ~1 mm^3 of tissue.
But the pattern of activity of thousands of voxels across cortex does contain reliable information! And a decent amount of it too, at least in sensory cortices.
Try it with a crude task - eg finger tapping. It’s pretty convincing.
Have you heard of time-domain reflectometry? A $20,000 multimeter could have the "impossible" feature you describe all but built in.